Recent advances in condensed matter theory have revealed that new and exotic phases of matter can exist in spin models (or more precisely, local bosonic models) via a simple physical mechanism, known as ”string-net condensation.” These new phases of matter have the unusual property that their collective excitations are gauge bosons and fermions. In some cases, the collective excitations can beh...

After having learned quite a lot about Lie groups, Lie algebras and their representation theory, it would be nice to see, where all this knowledge is put to use in physics. It might also be nice, to learn a bit about where finite groups appear in physics. To fill this gap, I will offer a seminar in the winter term 2010/11, which is entirely devoted to just these topics. Possible suggestions for...

We consider a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise, and one irreducible representation (IR) of the symmetry algebra splits into independent IRs describing a particle an its antiparticle only in the approximation when de Sitter energies are much less than the characteristic of the field. As a consequenc...

As argued in our previous papers, it would be more natural to modify the standard approach to quantum theory by requiring that i) one unitary irreducible representation (UIR) of the symmetry algebra should describe a particle and its antiparticle simultaneously. This would automatically explain the existence of antiparticles and show that a particle and its antiparticle are different states of ...

We have studied the low-energy excitation spectrum of a dimerized and frustrated antiferromagnetic Heisenberg chain. We use an analytic approach, based on a description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet (S=0) and...

In the nonrelativistic case of the Schrodinger equation, composite particles correspond to Regge poles in scattering amplitudes {poles in the complex plane of angular momentum). It has been suggested that the same may be true in relativistic theory. In that case, the scattering amplitude in which such a particle is exchanged behaves at high energies like s~~'& Lsinvo (t) 7 ', where s is the ene...